From Japan, it will be a bit pricey to dive Palau, Yap, and Chuuk. You might consider checking out Saipan as a less expensive an much closer destination, with possibly a side trip to Chuuk. I lived on Saipan from '86 to 2000, and logged over 650 hours underwater mostly on Saipan, with several trips to Chuuk, Palau, and Yap. One advantage to Saipan is that there is no need to pa for boat dives as the shore diving is excellent. I'd recommend you hook up with Rick Northern at Stingray Divers. Water temp is in the 80's ear round, with 100'+ vis. The best dive on the island is the Grotto; I dove it over 400 times while living there and never got bored. It's a huge pool inside a sinkhole accessed by a loooooong stone stairs. the pool goes to around 80' deep and has 3 tunels leading out to the ocean, with walls, caverns, dropoffs, lots of seafans, all kinds of fish, etc. If you do a night dive there, there are dozens of resident turtles that sleep inside and outside. The best time of year to go is in June or July, when the trade winds die down. This makes it a bit hotter, but allows access to sites like Banzai cliff which are normally too rough to dive at other times. If you don't mind a long walk over jaged rocks, the shore access is pretty dramatic, with a jump-in entrance through a hole in the roof of a cave for the daring, or a step off the shelf which is actually the roof of a cavern into 80' deep water, which quickly slopes to 125' at the corner of a dramatic wall. There's also some WWII junk that was dumped off the cliff there. Another little known good shore dives accessable only at that time of year is off San Vicente Village. I don't know if the operators take people there, but Rick might remember it; some people used to call it John's dropoff when I lived there, since I was the one that kinda discovered it. Again, it involves a worthwhild clamber down an steep overgrown rocky trail over the cliff down to the shelf where you step off for your entry. If you're not looking for a fancy resort, you can book a fairly reasonable room at a hotel like the Ocean View, but Rick will probably have recomendations. The island has been in recession since the late 90's so the prices should be reasonable and dive sites not too crowded. If you are more interested in local culture and sights than nightlive and tourest stuff, you'll do fine. A lot of the tourest oriented businesses have closed down in the last 5 years.
As for Chuuk, contact Gradfin Aisek or his sister Gardenia Walter at the Blue Lagoon dive shop and resort. They were personal friends, so I usually stayed at their homes, and didn't therefor spend much time in the hotels there. But compare prices at other hotels like the Truk Stop as far as accomodations. You shouldn't need to rent a car, as locals will give you a lift in their "taxi" pickup trucks cheap- it was only 50 cents to go anywhere you wanted last time I was there, but that was 6 years ago. Might be up to 75 cents now.Chuuk is still pretty backwater, so don't expect luxury accomodations. But you can't beat the wreck dives. Plan on many of the dives being fairly deep; 80-120'. Unless you just want to say you've done it, I wouldn't try to work in the San Francisco Maru, which sits at 200'. At that depth you will only have 10 minutes bottom time on the wreck, then three deco stops for a total of an hour of deco. It's an interesting wreck, but hardly worth an hour of hanging on a rope in midwater for just 10 minuetes bottom time. That being the deepest dive there, and it will cost you in bottom time available to do other shallower wrecks. The visability there isn't as good as Saipan due to a lot of plankton inside the lagoon, but still averages 40-50'. The vis does improve a bit if you go in January. Tell Gradfin and Gardenis John from Saipan says '"hello".